Output to Input Saturation Transformation: Demonstration and Application to Disturbed Linear Systems

In the case of linear systems, control law design is often performed so that the resulting closed-loop meets specific frequency requirements. However, in many cases, it may be observed that the obtained controller does not enforce time-domain requirements amongst which the objective of keeping an output variable in a given interval. In this article, a transformation is proposed to convert expected bounds on an output variable into time-varying saturations on the synthesized linear control law. It is demonstrated that the resulting closed-loop is stable and satisfies time-domain constraints in the presence of unknown bounded disturbance. An application to a linear ball and beam model is presented.